This can't be true: you can choose a point behind any sufficiently round satellite where it appears the same size as the star.

Perhaps it's the only place we know of on a planet's rocky surface. But most of our solar system's planets with moons don't have rocky surfaces, and we can't detect moons in other systems, so you really mean it's not true from the surface of Mars, Pluto or Charon.

Additionally, the moon varies in apparent diameter by about 13% from apogee to perigee, and the sun by about 3%. So while it might appear "exactly" the same size at some point in its orbit, mostly it's just within 5%.